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MODEL BASED OBSERVATION AND CONTROL OF DISTILLATION COLUMNS T. Liider, G. Wozny, G. Fieg and L. Jeromin H"lIkfl k(;aA . Pus/lach J JOO , D--/OOO Dii.\,Il'ldOlj J, FRG

Abstract. Two applications of mathematical process modeling to industrial scale distillation columns are discussed. In the fIrst part the stripping section of a methanol-water separation column is described with the help of the location of a temperature front. A simple linear state space model is used

to

design an observer

and state controller for the reboiler duty of the column. Its application is compared with experimental data obtained from an industrial distillation column with a PID-controller. In the second part an analytically reduced mathematical model for the estimation of the product composition in multicomponent distillation is presented. It is applied successfully to a fractionation plant consisting of three interlinked columns and is used for the purpose of diagnosis.

Keywords. Fluid composition control; modelling; state space methods; observers; state estimation; on-line operation; digital computer application; industrial distillation columns.

In the second part a dynamic model of a multicomponent distillation

INTRODUCTION

column

with

the

objective

of

product

composition estimation is presented. It is applied to a Distillation is one of the most important separation

fractionation plant consisting of three columns.

processes in chemical industry. During the last years the problem of an improved perfonnance of distillation columns METIlANOL-WATER SEPARATION COLUMN

with respect to the preservation of product purities and the reduction of energy consumption becomes important both in research and practice. As distillation columns are complex

The process. The plant under investigation here is a column

systems of high order with interacting control loops, the

with 50 valve trays operating at atmospheric pressure and

experience of the operating personnel is in general

heated directly with steam. The feed consists of methanol,

insuffIcient to handle these problems with the necessary accuracy.

isopropanol. The product requirements for the top and

water and impurities such as ethanol, propanol and bottom product are less than 0.1 weight percent water and methanol respectively. The impurities are removed with the

We show in this paper two industrial scale examples where the application of mathematical process models increases

help of a side stream. Figure 1 shows a flow diagram of the

the understanding of the process and consequently fonns the

column. Conventionally the steam flow is set by a

basis of an improved plant control.

PID-controller which controls the temperature in the

In the fIrst part of the paper a methanol-water separation

concentration as there is no adequate analyser available.

stripping section of the column instead of the bottom column is described comparing a model based control of the A rigorous simulation method (Wozny et al., 1987) has been

reboiler duty with a conventional PID control concept.

used to establish a connection between a changing operating

41

42

T. Uider

point and the migration of a combined heat and mass

1'1

{It.

Sets of constants K, - K4 for different working conditions of

transfer front in the stripping section of the column. This is

the column were estimated making use of the simulation

illustrated by the temperature profiles for changing operating

program. They resulted in different sets of design constants

conditions of the column in Fig. l. From this observation the

for the observer.

following process model was derived. Using the state control theory a controller can be designed which globally asymptotically stabilizes the system by linear Process model and controller design. To describe the state of

feedback of the state variables to the manipulated variable

the system a new variable was introduced, the locus of the

V. In order to achieve a controller robust enough for the

heat and mass transfer front (Eckelmann, 1980), which can

requirements of an industrial use the feedback parameters

be illustrated as the inflection point of the temperature

were adjusted with the controller on line but having started

profile in the stripping section. The first derivative of this

with reasonable values based on results of a pole placement

variable, the migration velocity of the front, is expressed by

strategy.

a simplified methanol balance around the stripping section

(1)

Comparison of performance. Figure 2 shows a comparison of the plant behaviour with the PID-controller and the state

The vapour flow rate in the column is given by the equation

controller \Wozny et aI., 1989). Figure 2a shows the trend of three major disturbance variables, the feed rate F, the feed concentration zF and the feed temperature T F' During the

dG K 2V=K,- +G

(2)

dt

time interval of five hours there are no significant changes detectable in the mean values of F and zF' Nevertheless the

Additonally

can be determind from a temperature

difference in the trend of the controller output V is evident (Fig. 2b). In contrast

measurement (Fig. 1)

to

the PID-controller the state

controller stabilizes the system quickly and persistent. This (3)

is reflected by the trend of the feed temperature (Fig. 2a). As the feed is preheated by the bottom product B the stable

These equations were used to design a linear state observer (Luenberger, 1964) for the unmeasured variables sand G from the given values for F, zF' R, and V. The feedback of the measurement T makes the observation error vanish

operating point of the column during the state controller operation stabilizes the feed temperature. Thus the use of the state controller leads to a safer and less energy consuming operation of the plant.

asymptotically (Fig. 1).

2

s

stage number

36

BalanceTi Section

51 70

90

O(

110

~

--~

(orrection IE-j; ---o

T

I

........ State Control System

J V

Fig. 1: Methanol-water separation column: process model and controller design

T

l\lodel Based Obse ryation and Control of Distillation Columns

-t3

to numerous operating points of the plant. Although analyser results (GC) for the feed and the three top products are only available with long responce times (30 to 45 min.) continous control of the product compositions is desired. Unfortunately in multicomponent systems concentration and temerature are not uniquely related. so that the wellknown application of temperature

instead

of

satisfactory. Presently

composition

control

is

not

the concentration is controlled

manually in consideration of the analyser results of the three distillates. Process simulation results for the distillation columns indicate that there is no temperature front detectable so that the main condition for the application of a process model of the frrst kind is violated. For this reason a different model was developed which allows the estimation of the product compositions without considerable dead times primarily to 60

increase the information available about the running process.

0,0

22

b)

PIO -

PI D-

(onlroller

~I_sl ale

1500

I

kg / h

I I

1200

I I

(anI roller _I_ (onlrolier

I I

I I

Process model. In order to achieve a simplified description of the process with physically significant parameters a

I I I I

model reduction procedure was chosen that is based on assumptions common in chemical engineering literature ( e.

I I

g. Smith. 1963; Benallou et al .• 1986; Rosendorf et al .•

I

1988).

I

I

From Fig. 4 the following dynamic component balance equations for the rectifying and stripping section of a

900

V

distillation column can be formulated 600

f-I

:r (L

HUjXj,i) = GYJ,i-LxI,i-Dxo,i+(l-q)FYF,i •

(4)

j:1

300 n

~(~ dt L 4

HUX JP' )

= Lx) ·-Gy) .-BxB +qFxF ' ,I

,I

,I

,I

(5)

j:f

h

i=I .....m , Fig. 2: Comparison of the plant behaviour: conventional and model based control of the methanol-water separation column

with a stage model of the process in mind and the vapour holdup on each stage neglected. To simplify the differential term the following is postulated dHUj

FRACTIONATION PLANT

dt

=0 .

j=2 .... n-1

The process. The second plant under investigation is a

dxJ,I

dxO,i

fractionation plant for fatty alcohols (Fig. 3). It consists of

dt

dt

(6)

j= 1... ,£-1

(7)

j=f....n

(8)

three multicomponent distillation columns with metal packings operating at vacuum conditions. The columns are connected directly as the bottom product of one column is used as the feed of the next one. Feed conditons varying over a wide range and changing product specifications lead

dxJ,I ..

dxB,i

dt

dt

T. Luder et al.

44 Introducing

XB,i f- I

HU R =

=0

and

dt

=0

(13a)

=0

(l3b)

or

LHUj

(9)

j=1

and

dxD,i

XD,i = 0 and

dt

n

Using these simplifications we get from eq_(11) and eq. (12) (10)

xD,i

we obtain

dHU R

dxD,i dt

+HU - - = FZF,i- DXD,i

(l4a)

B,_ I +HU _dx_

(l4b)

R

dt or

dHU R XD,i - - - +HU R dt

dxD,i dt

dHUs

(11)

XB,i~

s

dt

= FZF.i- BXB,i

For the non separated components the product concentration dHUs dt

+HU s

can be calculated from eq. (l4a) or eq. (14b). To solve the

dxB,i dt

model equations (11) and (12) for the separated components (12)

the unknown internal concentrations xI.i and Yl,i have to be expressed by the product concentrations xD.i and xB,i' Therefore the separation factors

This is the set of equations for components leaving the column with the distillate and the bottom flow ("separated components"). In multicomponent distillation however we often find operating conditions where further simplification

cR,i =

xLi (15)

xD.i

and

is justified. For components leaving the column almost completely with the distillate or the bottom product ("non separated components") we assume

cS,i =

YI.i (16)

xB,i

T

p

p

T P

p

P T

T

Fig. 3: Fractionation plant including measurements used for the composition estimation

45

Model Based Observation and Control of Distillation ColulIlns are

introduced.

Assuming

equimolal

overflow

and

thennodynamic eqilibrium on each stage cR.i and cS,i can be calculated from component balances around the top and the bottom of the column

D

cR,i =

L

[~(

G+(~-q)F )

j

n I=f·j

(

) +

f·1 kl,i

y.2

L

, f

f·1

G+(I-q)F

FZF',I (17)

2

>

kl,i n 1=2

v

+-cS,i = -

B G

[~

(

G

f·l+j G L+qF

) n·f

L+qF

Y nkl,i I=f

r1

Bxs',I

) +

Fig. 4: Balance sections of a distillation column: k. li

,n

>

I=f (IS)

CS,i = k",i

rectifying and stripping section

f

depends on how many components are regarded as non separated. The calculation is based on the knowledge of the column pressure and temperature profIle, the level

,n=f

fluctuations For mixtures of a homologous series of long chain

and

two

independent

flow

rates

from

measurements (Fig. 3).

n-alcohols it is convenient to use Raoult's law to describe the phase equilibrium. Thus for the separated components the equilibrium constants kj,i are calculated from the

Application. For the present application of the model

measured temperature and pressure profiles in the column by

described above a computer program was implemented in a process computer and the required measurements of all three

the Antoine equation.

columns were recorded in one minute time intervals. The set of equations was solved with an implicite Euler method

The mass balance equations

using time intervals of one minute as well. -

d

dt

HUR = G+(I-q)F-D-L

(19)

By successive calculation of the distillation in all three columns the estimated bottom flow rate and composition of

and

one column was used as the feed for the next one. In Fig. 5 the results of the composition estimation for the top product (20)

of the second column is compared to the analyser results during a time interval of 10 hours. Figure 5a shows the oscillating trend of the calculated feed rate (bottom flow rate

and the steady state evaporator balance

V

llhLG,v

G

llhLG,G

of the fIrst column) and the measured distillate rate, which is (21)

caused by the level control. The lower curve shows the trend of the concentration of the

n-alcohol CIS (separated

component). The calculated values (continous line) are complete the model.

compared to the analyser results (marked with. ). Figure 5b

The reduction of this set of equations leads to a system of

of the non separated n-alcohol C14 ( A ) and the separated

shows the signifIcant change in the measured concentrations less than 2 m equations for the unknown product

n-alcohol C16 ( . ) during the fIrst part of the interval which

concentrations of the distillation column. The exact number

is

well

reproduced

by the calculated concentrations

46

T. Lilder et al.

.., .... ID .... u

a)

~

,.,

..,

J::

J::

....~ ~

~~8~8~ 0

1Q

~

8

ID

(\/

0 0 0 III

8 to

0 0

8

III

....

III -t'

0 0

0 0

....

0 -t'

8

0

0 0

.i-

0

8

8

8

C\i

III

~

0 0

0

0 0 0

0

(')

+

~

A

I

0.00

I

1.00

I

2.00

I

3.00

I

4.00

I

5.00

I

I

I

6.00

7.00

8.00

I

I 7.00

8.00

I

9.00

I

10.00

time Ch]

.., ....

b)

M

~

....

....

-t' .... u

~

ID

u

~~8~

8!

&0

0 0

0 0

~

.i-

0 0

0 0

.ien

M

0 0

0 0

SI

C\i

0 0

0

0

~

8 IB

0 0 0

+

A

I

0.00

I

1.00

I

2.00

I

3.00

I

4.00

I

5.00

6.00

I

I

9.00

I

10.00

time Ch] Fig. 5: Distillate of the second column of the fractionation plant: comparison of measured and calculated composition a) calculated feed rate (----A), measured distillate rate (-+), calculated distillate concentration Cl8 (~),

and measured distillate concentration Cl8 ( • )

b) calc. dist. cone. C14 (-.6), meas. dist. cone. C14 (A), calc. dist. cone. C16 (-+), meas. dist. cone. C16 (_)

Model Based Observation and Control of Distillation Columns (continous lines). Generally the deviation between measured

z

and calculated values is smaller than one percent.

l!.hLG heat of vaporization

mole fraction feed

A detailed description of the program and these results is given by Ludwig (1989). One run of the program for three

SUBSCRIPTS

columns and a real time interval of 10 hours requires a calculation time of approx. 13 minutes CPU on a MicroV AX

B

bottom

II microcomputer.

D

distillate

f

F

fIrst stage of the stripping section feed

G

gas

CONCLUSIONS

internal component

The fIrst part of this paper shows that the application of

stage

linear observer and linear state control theory in combination with an appropriate simple process model can lead to a

n

signifIcant improvement in plant operation even for

R

experienced

S V

industrial

scale

distillation

columns.

Consequently we presently investigate the question whether

last theoretical stage of the column (evaporator) rectifying section stripping section steam

the whole column can be described and controlled in the same way as shown for its stripping section. REFERENCES In the second part a dynamic model for the estimation of the product compositions in multicomponent distillation is introduced which is not limited to a particular working point or column structure. The results of the application to the process show that the model describes the plant behaviour

Benallou, A., D. E. Seborg, D. A.

Mellichamp (1986).

Dynamic compartmental models for separation processes. AIChE Journal, 32, 1067-1078. Eckelmann,

W.

(1980).

Erfaltrungen

for the operation of the plant. Furthermore it can form the

Destillationskolonnen. Regelungstechnische Praxis, 22, 120-126.

basis of the development of an automatic composition

die

Regelung

einem

Zustandsbeobachter

control for multicomponent distillation columns.

fiir

mit

well. Thus it can be used to provide important information

von

Ludwig, B. (1989). Unpublished student thesis. Institut fUr Thermische Verfahrenstechnik der TU Clausthal, West Germany.

NOTATION

Luenberger, D. (1964). Observing the state of a linear

B

bottom flow rate

system. IEEE Trans. on Military Electronics, .!!., 74-80.

c

separation factor

Rosendorf, P., M. Kubicek, and 1. Schongut (1988). On-line

D

distillate flow rate

optimization of a rectifIcation column. Comput.

F

feed rate

chem. Engng., 12, 199-203.

G

gas flow rate in the column

HU

liquid hold up

Smith, B. D. (1963). Design Qf equlibrium stage processes. McGraw-Hill, New York. Chap. 8. Wozny, G., G. Fieg, L. Jeromin, M. Kohne and H. Giilich

K

constant

k

equilibrium constant

(1989). Design and analysis of a state observer for

L m

liquid flow rate in the column number of components

the temperature front of a rectifIcation column.

n

number of theoretical stages

p

pressure

distillation with high product purities. Chem. Eng.

q

thermal state of the feed

and Technology, l, 338-348.

R

reflux rate locus of the front

T

temperature time

V

steam flow rate

x

mole fraction liquid

y

mole fraction gas

Chem. Eng. and Technology, in press. Wozny, G., W. Win and L. Jeromin (1987). Dynamics of

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